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Striped phases in which spin and charge separate into different regions in the material have been proposed to account for the unusual properties of the high-Tc cuprate superconductors. The driving force for a striped phase is the charge distribution, which self-organizes itself into linear regions. In the highest Tc materials such regions are not static but fluctuate in time. Neutrons, having no charge, cannot directly observe these fluctuations but they can be observed indirectly by their effect on the phonons. Neutron scattering measurements have been made using a specialized technique to study the phonon line shapes in four crystals with oxygen doping levels varying from highly underdoped to optimal doping. It is shown that fluctuating charge stripes exist over the whole doping range, and become visible below temperatures somewhat higher than the pseudogap temperature.